A Three-Dimensional Subspace Algorithm Based on the Symmetry of the Approximation Model and WYL Conjugate Gradient Method
In this paper, a three-dimensional subspace method is proposed, in which the search direction is generated by minimizing the approximation model of the objective function in a three-dimensional subspace. The approximation model of the objective function is not unique, and alternatives can be chosen...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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MDPI AG
2023-06-01
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| Series: | Symmetry |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2073-8994/15/6/1207 |
| _version_ | 1797592547670884352 |
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| author | Guoxin Wang Shengwei Yao Mingyang Pei Jieqiong Xu |
| author_facet | Guoxin Wang Shengwei Yao Mingyang Pei Jieqiong Xu |
| author_sort | Guoxin Wang |
| collection | DOAJ |
| description | In this paper, a three-dimensional subspace method is proposed, in which the search direction is generated by minimizing the approximation model of the objective function in a three-dimensional subspace. The approximation model of the objective function is not unique, and alternatives can be chosen between a symmetric quadratic model and a conic model by specific criteria. Moreover, the idea of a WLY conjugate gradient method is applied to characterize the change of gradient direction between adjacent iteration points. The strategy of initial stepsize and nonmonotone line search are adopted, and the global convergence of the presented algorithm is established under mild assumptions. In numerical experiments, we use a collection of 80 unconstrained optimization test problems to show the competitive performance of the presented method. |
| first_indexed | 2024-03-11T01:52:46Z |
| format | Article |
| id | doaj.art-10f8f3d3876c437baef5f2a5ef7c5d14 |
| institution | Directory Open Access Journal |
| issn | 2073-8994 |
| language | English |
| last_indexed | 2024-03-11T01:52:46Z |
| publishDate | 2023-06-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Symmetry |
| spelling | doaj.art-10f8f3d3876c437baef5f2a5ef7c5d142023-11-18T12:50:57ZengMDPI AGSymmetry2073-89942023-06-01156120710.3390/sym15061207A Three-Dimensional Subspace Algorithm Based on the Symmetry of the Approximation Model and WYL Conjugate Gradient MethodGuoxin Wang0Shengwei Yao1Mingyang Pei2Jieqiong Xu3School of Mathematics and Information Science, Guangxi University, Nanning 530004, ChinaGuangxi (ASEAN) Financial Research Center, Guangxi University of Finance and Economics, Nanning 530007, ChinaSchool of Mathematics and Information Science, Guangxi University, Nanning 530004, ChinaSchool of Mathematics and Information Science, Guangxi University, Nanning 530004, ChinaIn this paper, a three-dimensional subspace method is proposed, in which the search direction is generated by minimizing the approximation model of the objective function in a three-dimensional subspace. The approximation model of the objective function is not unique, and alternatives can be chosen between a symmetric quadratic model and a conic model by specific criteria. Moreover, the idea of a WLY conjugate gradient method is applied to characterize the change of gradient direction between adjacent iteration points. The strategy of initial stepsize and nonmonotone line search are adopted, and the global convergence of the presented algorithm is established under mild assumptions. In numerical experiments, we use a collection of 80 unconstrained optimization test problems to show the competitive performance of the presented method.https://www.mdpi.com/2073-8994/15/6/1207unconstrained optimizationsubspaceconic modelglobal convergence |
| spellingShingle | Guoxin Wang Shengwei Yao Mingyang Pei Jieqiong Xu A Three-Dimensional Subspace Algorithm Based on the Symmetry of the Approximation Model and WYL Conjugate Gradient Method Symmetry unconstrained optimization subspace conic model global convergence |
| title | A Three-Dimensional Subspace Algorithm Based on the Symmetry of the Approximation Model and WYL Conjugate Gradient Method |
| title_full | A Three-Dimensional Subspace Algorithm Based on the Symmetry of the Approximation Model and WYL Conjugate Gradient Method |
| title_fullStr | A Three-Dimensional Subspace Algorithm Based on the Symmetry of the Approximation Model and WYL Conjugate Gradient Method |
| title_full_unstemmed | A Three-Dimensional Subspace Algorithm Based on the Symmetry of the Approximation Model and WYL Conjugate Gradient Method |
| title_short | A Three-Dimensional Subspace Algorithm Based on the Symmetry of the Approximation Model and WYL Conjugate Gradient Method |
| title_sort | three dimensional subspace algorithm based on the symmetry of the approximation model and wyl conjugate gradient method |
| topic | unconstrained optimization subspace conic model global convergence |
| url | https://www.mdpi.com/2073-8994/15/6/1207 |
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